WO2022057700A1 - 一种多艘无人测量船艇覆盖路径规划方法 - Google Patents
一种多艘无人测量船艇覆盖路径规划方法 Download PDFInfo
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- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/02—Control of position or course in two dimensions
- G05D1/0206—Control of position or course in two dimensions specially adapted to water vehicles
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Definitions
- the invention belongs to the field of path planning, and more particularly, relates to an optimized method for planning coverage paths of multiple unmanned surveying vessels (CCIBA*).
- Unmanned Surface Vessel It has the advantages of low power consumption, flexible operation and no need for manned people, and it is very useful in water depth sounding tasks.
- the Unmanned Surface Mapping Vehicle (USMV) has a larger operating range and a more complex water environment, which puts forward higher requirements for the efficiency and robustness of the coverage path planning algorithm.
- the present invention proposes a coverage path planning method for multiple unmanned surveying vessels, which improves the coverage rate and coverage effect of unmanned surveying vessels in complex operating environments, and improves the performance of unmanned surveying vessels. efficiency of the boat.
- a method for planning a coverage path of multiple unmanned surveying vessels including:
- the static map is used to reflect the environmental information.
- the submap represents the regional map formed after the rasterized static map is divided into regions, and the overall map represents the integration and iteration of the submap;
- step (1) comprises:
- each unmanned surveying vessel is in the default starting position, the state is O, the coordinate conversion grid index of the static map is established, the grid status update is carried out in each sub-map, and the 0 ⁇ L-level assignment, USMV i outputs the tn command, at the same time, USMV i records and transmits its own position ⁇ and obstacle information ⁇ , each USMV i starts to update its grid state list GT_list independently, and starts the collaborative coverage task, among which, tn indicates that the USMV is instructed to be in a normal state so that it can perform normal coverage tasks in the sub-region.
- a list of behavior strategies is defined: BS ⁇ ex 1 ,ex 2 ,ex 3 ,ex 4 ⁇ , where ex 1 ,ex 2 ,ex 3 ,ex 4 correspond to the area segmentation, There are four situations of backtracking transfer, area exchange and obstacle joint identification.
- the path planning determines the BS first, and outputs the te or th state if any of the conditions are met, and the cross-domain is involved based on the Planning output tp m , if it does not meet any situation of BS, execute path planning independently, and output tn or tc state, where tp m represents the grid index value of the location of the next target point of USMV in the overall map, and te represents guidance
- tp m represents the grid index value of the location of the next target point of USMV in the overall map
- te represents guidance
- the USMV starts to switch areas and coordinate the coverage tasks between the areas. th indicates to guide the USMV to continue the coverage task in the new area.
- the sub-map and the overall map are divided into regions based on task performance, including:
- Each grid ⁇ in the free space PF that defines the overall task area P is overscanned by at least any USMV i :
- Y( ⁇ ,i) represents the grid limit
- the overall coverage path, overall coverage time, individual coverage performance and overall coverage rate are mainly considered.
- the d cost and t cost of the initial mission area are estimated according to the performance index Hi of USMV i , where, d cost represents the coverage path, t cost represents the coverage time, d cost will be further revised according to the distribution of obstacles, t cost will be adjusted taking into account the equipment carried by the USMV, and finally output the reassigned sub-area, where, Represents the overall cost model of multi-boat coverage, k 1 represents the coverage path cost coefficient, k 2 represents the coverage time cost coefficient, P i (d cost ) represents the estimated coverage path in the Pi area, and P i (t cost ) represents the forecast in the Pi area.
- Estimated coverage time the overall cost model of multi-boat coverage
- k 1 represents the coverage path cost coefficient
- k 2 represents the coverage time cost coefficient
- P i (d cost ) represents the estimated coverage path in the Pi area
- P i (t cost ) represents the forecast in the
- step (2) comprises:
- Level map stage for each submap Give priority to potential energy row by row to ensure the complete coverage path of USMV i in each submap;
- ⁇ represents the grid sequence number of the current location of the USMV
- BV ⁇ refers to the assignment of the number of grid sequences ⁇ in the BL top-level map
- the detection area of USMV in the grid map is recorded as D 0 ( ⁇ ), ⁇ D 0 ( ⁇ ), D 0 ( ⁇ ) contains With all the grid information that the USMV can perceive at the current position, for any grid ⁇ 0 in D 0 ( ⁇ ), if the connection with ⁇ does not pass through the fz or obs state grid, and its own potential energy value is positive , then define its set as the priority field Define the grids located in the north and south directions
- a BS determination is performed before upgrading the map level. If it is determined that the above conditions are inconsistent, it is determined that the USMV i is in a local optimal state at this time. Before upgrading the map level, a BS determination is performed. If it conforms to the collaborative strategy, the preset action is started, the te command is output, and the submap is updated. Reallocate the sub-area P i ; if it does not meet any of the conditions in the BS, turn on the high-level BL map stage to start routing, and output the tr command.
- step (3) includes:
- step (4) includes:
- a computer-readable storage medium on which a computer program is stored, and when the computer program is executed by a processor, implements the steps of any one of the above-mentioned methods.
- the invention draws on the traditional coverage path planning method, conducts in-depth research on the collaborative coverage path planning of multiple unmanned surveying vessels, and designs a coverage path planning method for multiple unmanned surveying vessels (Cooperative Coverage IBA*, CCIBA*), which is an unmanned surveying vessel.
- the vessel plans an efficient and high-quality scanning path.
- the simulation test results show that the performance of CCIBA* is significantly improved compared with the existing methods in terms of path length, number of turns, number of cells and coverage.
- FIG. 1 is a schematic flowchart of a method for planning a coverage path of multiple unmanned surveying vessels provided by an embodiment of the present invention
- FIG. 2 is a schematic flowchart of another method for planning a coverage path of multiple unmanned surveying vessels provided by an embodiment of the present invention
- FIG. 3 is a schematic diagram of a typical behavior strategy provided by an embodiment of the present invention.
- FIG. 4 is a flowchart of a USMV i task decomposition provided by an embodiment of the present invention.
- the purpose of the present invention is to provide a coverage path planning method CCIBA* for multiple unmanned surveying vessels.
- the CCIBA* algorithm is an extension on the basis of IBA* (Improved BA*). Both CCIBA* and IBA* are based on traditional The improvement of the BA* algorithm improves the coverage rate and coverage effect of unmanned surveying vessels in complex operating environments, and improves the operational efficiency of unmanned surveying vessels.
- FIG. 1 is a schematic flow chart of a method CCIBA* for coverage path planning for multiple unmanned surveying vessels provided by an embodiment of the present invention, and the method includes: O stage, level map stage, Level map stage and E stage.
- CCIBA* is divided into 2 processes according to the above 4 stages: offline planning and online planning.
- the sub-areas are divided based on the task performance, and four typical cooperative behavior strategies are established, including area segmentation, retrospective transfer, area exchange and joint obstacle identification.
- the online planning specifically includes: task decomposition of the scanning scene and update of the scanning scene map.
- FIG. 2 is a schematic flowchart of another method CCIBA* for coverage path planning for multiple unmanned surveying vessels provided by an embodiment of the present invention, which specifically includes the following steps:
- Stage O import the static map in the initialization stage, initialize the grid state according to the static map, establish the sub-map and the overall map synchronously, and divide the sub-map and the overall map respectively based on the task performance;
- the static map is used to reflect the environmental information, that is, the navigation map of the unmanned surveying boat (nautical map or river map).
- Both the sub-map and the overall map reflect the navigation environment information of the survey boat.
- the sub-map represents the rasterized static map and the regional map formed by the CCIBA* algorithm for regional division.
- the overall map represents the integration and iteration of the sub-maps.
- the sub-map and the overall map are divided into regions based on the task performance, including:
- each grid ⁇ in the free space PF of the overall task area P is specified, and at least any USMV i performs an overscan task:
- Y( ⁇ ,i) represents the grid limit
- ue represents the free space where the bathymetric task is not completed.
- k 1 represents the coverage path cost coefficient
- k 2 represents the coverage time cost coefficient
- P i (d cost ) represents the estimated coverage path in the Pi area
- P i (t cost ) represents the forecast in the Pi area. Estimated coverage time.
- S102 Level map stage: according to submaps with general map The USMV i of each sub-area P i outputs its own position information ⁇ and obstacle information ⁇ , and transmits it to and update Then perform path planning and find the target point tp;
- BL 0 ,...BL L represents each dynamic map level BaseLayer, L is the highest level, and the total map is and the submap for
- S103 Level map stage: When falling into a local optimum, update the map level layer by layer, find the target point tp in the corresponding level, make a BS judgment, and send the tr command to the USMV i in the sub-region Pi , where the BS judgment means Cooperative behavior strategy determination, tp represents the grid index value of the location of the next target point of the USMV, and the tr command represents that the USMV is in the Travel state, and the abnormal task state after reaching the local optimum;
- BS ⁇ ex 1 ,ex 2 ,ex 3 ,ex 4 ⁇ , ex 1 ,ex 2 ,ex 3 ,ex 4 correspond to area segmentation and retrospective transfer in the cooperative behavior strategy, respectively , area exchange and obstacle joint identification of four situations.
- Path planning determines the BS first, and outputs the te or th state if it meets any of the conditions. Planning output tp m ; if it does not meet any situation of BS, execute path planning independently, and output tn or tc state, where tn indicates to guide USMV to be in Normal state, so that it can perform normal coverage tasks in the sub-area, and tc indicates to guide USMV Start a sounding mission.
- typical collaborative behavior strategies specifically include:
- the dashed line represents the area division boundary
- the irregular figure represents the obstacle
- the dot-dash line represents the area exchange or redistribution involved in the cooperative behavior strategy.
- the area segmentation scenario involves temporary allocation of small areas and update of submaps.
- the P2 area when USMV enters the small Area formed by obstacles and area boundaries, it will face potential losses in two aspects: First, according to the obstacle processing strategy of the IBA* algorithm, when entering the area, it is subject to narrow and long terrain. Influence, the cost of bypassing the barrier increases; second, in the case of non-interference, entering the region may fall into a local optimum. In the case of preliminary identification of obstacle edges in the P1 area, this strategy incorporates the small Area area in the P2 area into the P1 area, so that the USMV can "follow the trend" to perform the Area area coverage task under the condition of ensuring continuous coverage action. Due to the small area of this area, it has little impact on the task allocation of the two, and the completion time is basically unchanged.
- the backtracking transition scenario involves the backtracking area caused by the trend change of the path direction.
- the IBA* algorithm will generate potential backtracking regions.
- USMV 1 in the P 1 area starts to bypass the obstacle shortly after starting from the starting position. From this time until the USMV 1 goes out of bounds in the lower left area, the Area area is still in the state of unexplored coverage . Therefore, this strategy divides the Area into the P2 area, so that USMV 2 in this area continues to enter the Area to perform additional coverage actions, reducing the backtracking cost of USMV 1 .
- the area exchange scenario involves the exchange allocation of a larger area. Due to the influence of obstacles and boundaries, a large area is split into the P 2 area. Continuing to execute the Area_2 area task will increase the path cost and computational cost of the USMV 2 in the P 2 area. At this time, the Area_2 area happens to be located in the P 2 area. The main coverage path direction of the 1 area, and the Area_1 area is located in the main coverage path direction of the P2 area. Therefore, the policy swaps Area_1 and Area_2 in the P 1 and P 2 regions. In this case, the coverage time and task volume are basically unchanged, and based on roughly the same obstacle cost, the impact on the path length is also small.
- the joint obstacle recognition scene is mainly aimed at the processing of obstacles. Due to the independent sub-area map update, the obstacle-circumvention paths of the individual S P_1 and S P_1 segments are incomplete for each USMV, and the determination of obstacles may be omitted, thereby affecting the update of the overall area map. Therefore, when the coverage task is executed At the same time, the process of joint judgment of obstacles is additionally added.
- the task decomposition of the scanning scene includes:
- G m represents the list of total map rasters, Represents the individual space of the total map grid, N represents the maximum number of grids, represents the overall task based on the overall grid list G m , R i represents the sub-task numbered i , I represents the upper bound of the number of tasks Pi, which is consistent with the number of USMVs participating in the task, and the superscript m has no specific physical meaning.
- State definition The state is the basic state of multi-boat coverage path planning, reflecting the overall process and internal adjustment of the task:
- S m represents the overall state list
- O represents the state start
- Q ini represents the initial task assignment
- Q re represents the coordination task assignment
- E represents the end state
- COM represents the computation state.
- ⁇ represents the backtracking list
- ⁇ i represents the backtracking list of each sub-region.
- tp m represents the grid index value of the location of the USMV next target point in the overall map
- N m represents the set of natural numbers
- OC m represents the USMV task command in the overall map, which has higher authority and priority than sub-regions
- tn indicates that the USMV is in a normal state to perform normal coverage tasks in the sub-region
- te indicates that the USMV is instructed to start switching regions and coordinate the coverage task between regions
- th indicates that the USMV is instructed to continue the coverage task in the new region;
- the system state list S is initialized.
- the Q ini state starts first, the task area is initialized, and the task area of each USMV i is roughly divided according to the task performance evaluation.
- the tn command is output to each USMV i , and the sub-area coverage task is completed inside it according to the IBA* algorithm, which is recorded as the COM state.
- USMV i continuously records and feeds back ⁇ and ⁇ , and generates obstacle information in real time. According to the cooperative behavior matching, if the redistribution conditions are met at this time, the system will be switched to the Q re state, and the sub-area will be re-allocated.
- USMV i The affected USMV i will be adjusted to the te state, and the coverage path planning algorithm will generate tpm . Jump out of the original area, and after reaching the designated starting point, guide to turn on the th state. USMV i records the state value CS of the experienced grid and the state value of the Pi area in each area action
- the map update of the scanning scene includes two parts: the general map update and each sub-region map update, wherein the general map has a higher priority and authority, and can intervene in necessary processes.
- the sub-region map update process is in an independent state, and each USMV i updates the overall map at the same time in action and submaps After P i and R i are assigned regions and tasks, each Independent update to complete multiple USMV coverage tasks, It mainly acts on the cooperative behavior of USMV i between regions, so that USMV i has a more reasonable choice when searching for target points by upgrading the map level in the sub-region, thereby saving the overall coverage time and reducing the impact of the tr state and te state on the path length. negative impacts.
- the grid map level with the highest precision is first established in the global map. Subsequently, in On the basis, continue to establish the map level of each sub-interval Its specific area is determined by the initial division of the overall area P. exist and On the basis of the level established, continue to execute the upgrade instructions.
- the O stage in step S101 includes:
- each unmanned surveying vessel is in the default starting position, the state is O, the coordinate conversion grid index of the static map is established, the grid status update is carried out in each sub-map, and the 0 ⁇
- USMV i outputs the tn command.
- USMV i records and transmits its own position ⁇ and obstacle information ⁇ .
- Each USMV i starts to update its grid state list GT_list independently, and starts the cooperative coverage task.
- step S102 The level map stage specifically includes:
- Level map stage for each submap Give priority to potential energy row by row to ensure the complete coverage path of USMV i in each submap;
- BV ⁇ > 0 and It is consistent with the action of the IBA* algorithm of a single USMV , and the relative optimal path is selected by calculating the potential cost value J (tp). ⁇ N or ⁇ S azimuth, select the relative optimal path to complete the obstacle bypass path of each interval Pi by calculating the potential cost value J(tp), and start the ex 4 process at the same time, ⁇ represents the grid sequence number of the current location of the USMV , BV ⁇ refers to the assignment of the grid sequence number ⁇ in the BL top-level map;
- the detection area of USMV in the grid map is denoted as D 0 ( ⁇ ), ⁇ D 0 ( ⁇ ), and D 0 ( ⁇ ) contains all the grid information that the current position of USMV can perceive.
- D 0 ( ⁇ ) contains all the grid information that the current position of USMV can perceive.
- a BS determination is performed before upgrading the map level. If it is determined that the above conditions are inconsistent, it is determined that the USMV i is in a local optimal state at this time. Before upgrading the map level, a BS determination is performed. If it conforms to the collaborative strategy, the preset action is started, the te command is output, and the submap is updated. Reallocate the sub-area P i ; if it does not meet any of the conditions in the BS, turn on the high-level BL map stage to start routing, and output the tr command.
- step S103 The level map stage specifically includes:
- the E stage in step S104 specifically includes:
- Stage E is the end stage, according to When the USMV i of all sub-regions P i are sent back to FN i , it is determined that the coverage task of the entire task region P is over, and the missing regions are reviewed through all the detected environmental information to generate coverage information.
- the performance of the CCIBA* method of the present invention in terms of path length, turning times and coverage rate is reduced by about 16.5% and 5.1% respectively in terms of turning times; the number of units Respectively decreased by 58.3%, 44.4%; coverage increased by about 2.1%, 7.6%.
- the path length does not increase significantly compared with the BA* algorithm, and is reduced by about 10.76% compared with the Boustrophedon algorithm that achieves complete coverage.
- the present application also provides a computer-readable storage medium, such as flash memory, hard disk, multimedia card, card-type memory (eg, SD or DX memory, etc.), random access memory (RAM), static random access memory (SRAM), read-only memory Memory (ROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Programmable Read-Only Memory (PROM), Magnetic Memory, Magnetic Disk, Optical Disc, Server, App Store, etc., on which computer programs are stored, programs When executed by the processor, the method for planning the coverage paths of multiple unmanned surveying vessels in the method embodiment is implemented.
- a computer-readable storage medium such as flash memory, hard disk, multimedia card, card-type memory (eg, SD or DX memory, etc.), random access memory (RAM), static random access memory (SRAM), read-only memory Memory (ROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Programmable Read-Only Memory (PROM), Magnetic Memory, Magnetic Disk, Optical Disc, Server, App Store, etc.
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Abstract
一种多艘无人测量船艇覆盖路径规划方法，属于路径规划领域，包括：根据静态地图初始化栅格状态，同步建立子地图与总地图(S101)；根据子地图与总地图各个子区域的USMV i输出自身位置信息及障碍物信息，传递给BLl
i，更新 BLl
m；定义行为策略列表BS；路径规划优先判定BS，若符合任一情形则输出te或th状态，涉及跨域则基于BLl
m规划输出tp m；若不符合则独立执行路径规划，输出tn或tc状态(S102)；陷入局部最优时，则向上逐层更新地图层级，并在对应层级中寻找tp，进行BS判定，输出tr指令(S103)，若最高层级仍未找到目标点，检查各个CSPiϵ{FNi，UFNi}，判定结束(S104)。由此，能够提升多艘无人测量船艇复杂作业环境下覆盖率和覆盖效果，提高无人测量船艇的作业效率。
Description
本发明属于路径规划领域，更具体地，涉及一种优化的多艘无人测量船艇覆盖路径规划方法(CCIBA*)。
水下地形勘探和测量作业是保障水路运输安全的基本条件，其需求日趋旺盛。传统水域测量作业主要由有人船艇搭载测量设备在作业水域往复航行实现，近年来，随着人工智能技术和船舶工业的发展，无人船艇(Unmanned Surface Vessel,USV)凭借着吃水浅、能耗低、操纵灵活且无需载人等优势，在水域测深任务方面大显身手。
目前覆盖路径规划研究多集中于地面移动机器人领域。与地面移动机器人相比，无人测量船艇(Unmanned Surface Mapping Vehicle,USMV)作业范围更大、水域环境更复杂，对覆盖路径规划算法的效率和鲁棒性提出了更高要求。
发明内容
针对现有技术的以上缺陷或改进需求，本发明提出了一种多艘无人测量船艇覆盖路径规划方法，提升无人测量船艇复杂作业环境下覆盖率和覆盖效果，提高无人测量船艇的作业效率。
为实现上述目的，按照本发明的一个方面，提供了一种多艘无人测量船艇覆盖路径规划方法，包括：
(1)在初始化阶段导入静态地图，根据静态地图初始化栅格状态，同步建立子地图与总地图，并基于任务性能分别对子地图和总地图进行区域划分，其中，静态地图用于反映环境信息，子地图表示栅格化的静态地图 进行区域划分后形成的区域地图，总地图表示子地图的整合与迭代；
(2)根据子地图
与总地图
中各个子区域P
i的USMV
i输出自身位置信息ω及障碍物信息η，传递给
并更新
然后进行路径规划，寻找目标点tp，tp表示USMV下一目标点所处位置的栅格索引值，tr指令表示USMV处于Travel状态，达到局部最优后的非正常任务状态；
(3)陷入局部最优时，则向上逐层更新地图层级，并在对应层级中寻找目标点tp，进行BS判定，并向子区域P
i的USMV
i发送tr指令，其中，BS判定表示协同行为策略判定；
(4)若最高层级仍未找到目标点，检查各个
判定结束，其中，
表示USMV
i在所处的当前子区域P
i中的区域测深任务状态，其中，FN
i代表已完成，UFN
i代表未完成。
在一些可选的实施方案中，步骤(1)包括：
起始时各艘无人测量船艇均处于默认起始位置，状态为O，建立静态地图的坐标转换栅格索引，分别在各子地图开展栅格状态更新，并依次更新全部地图的0～L级的赋值，USMV
i输出tn指令，与此同时，USMV
i记录及传递自身位置ω及障碍物信息η，各个USMV
i开始独立更新各自的栅格状态列表GT_list，开始协同覆盖任务，其中，tn表示指导USMV处在正常状态，使其在子区域内执行正常覆盖任务。
在一些可选的实施方案中，定义行为策略列表：BS∈{ex
1,ex
2,ex
3,ex
4}，ex
1,ex
2,ex
3,ex
4分别对应协同行为策略中区域分割、回溯转移、区域交换和障碍物联合识别4种情形。
在一些可选的实施方案中，路径规划优先判定BS，若符合任一情形则输出te或th状态，涉及跨域则基于
规划输出tp
m，若不符合BS任一情形则独立执行路径规划，输出tn或tc状态，其中，tp
m表示USMV下一目 标点所处位置在总地图中的栅格索引值，te表示指导USMV开始切换区域，协调区域间的覆盖任务，th表示指导USMV在新的区域继续覆盖任务。
在一些可选的实施方案中，基于任务性能分别对子地图和总地图进行区域划分，包括：
建立多USMV集合，U＝{USMV
i|1≤i≤I}，I表示USMV数量，协同覆盖的核心目标是使i艘USMV在充分发挥效率的前提下实现对整体任务区域P全部遍历；
根据USMV
i个体的性能或执行覆盖任务的能力，提出任务性能指数H
i,i＝1,...I，其大小取决于USMV携带的传感器性能、任务职能及能耗限制等，且
根据USMV数目将整体任务区域P划分为I个部分，其中，每个部分对应一个USMV所处区域，各部分以其所占面积百分比表示，其中，各部分表示为：P
i,i＝1,...I，0＜P
i＜1且
规定整体任务区域P的自由空间P
F中的每个栅格α，至少被任一USMV
i执行过扫描任务：
其中，由0＜P
i＜1且
确定自由空间，Y(α,i)表示栅格限制，
表示BL级地图中t时刻下的栅格α赋值；
对于多无人船艇协同覆盖，主要考虑整体覆盖路径、整体覆盖时间、单体覆盖性能及整体覆盖率，首先根据USMV
i的性能指数H
i估算初始任务区域的d
cost和t
cost，其中，d
cost表示覆盖路径，t
cost表示覆盖时间，d
cost将根 据障碍物的分布情况进行进一步修正，t
cost则在考虑USMV携带装备的情况下调整，最终输出重新分配后的子区域，其中，
表示多艇覆盖总体代价模型，k
1表示覆盖路径代价系数，k
2表示覆盖时间代价系数，P
i(d
cost)表示P
i区域预估覆盖路径，P
i(t
cost)表示P
i区域预估覆盖时间。
在一些可选的实施方案中，步骤(2)包括：
在
级地图阶段对各个子地图
逐行赋予势能优先级，保证各子地图中USMV
i的完整覆盖路径；
若BV
ω＞0且
则与单USMV的IBA*算法行动一致，通过潜在代价值J(tp)计算选择相对最优路径，同样的，若ω
N及ω
S中的一侧临近障碍物，则优先选取临近障碍物的ω
N或ω
S方位，通过潜在代价值J(tp)计算选择相对最优路径完成各个区间P
i的绕障路径，同时开启ex
4过程，ω表示USMV当前所处位置的栅格序列数，BV
ω是指BL最高层地图中栅格序列数ω的赋值；将USMV在栅格地图中的探测领域记为D
0(ω)，ω∈D
0(ω)，D
0(ω)中包含了USMV当前位置能感知到的所有栅格信息，对于D
0(ω)中的任一栅格α
0，若与ω的连线不经过fz或obs状态栅格，且自身势能值为正值，则将其集合定义为优先领域
定义D
0(ω)中位于北、南两个方向的栅格为ω
N及ω
S；
若BV
ω＞0，ω
N及ω
S中有且只有一侧为ue状态，另一侧为禁区，则开启tc指令，以指导USMV
i开始测深任务，同时更新
和
若BV
ω＝0,
则USMV
i开始转向下一阶段的遍历，将F
0中
值最大的α
0作为tp点，α
0表示栅格索引；
若以上情形均判定不符，则认定USMV
i此时处于局部最优的状态，在升级地图层级前，进行BS判定，若符合协同策略，则开始运行预设动作，输出te指令并更新子地图，重新分配子区域P
i；若不符合BS中的任意一种情形，则开启高BL级地图阶段开始寻径，输出tr指令。
在一些可选的实施方案中，步骤(3)包括：
在
级地图阶段，逐级提高地图等级，在高级地图中继续寻找势能值最大的地图栅格，同时计算其潜在代价值J(tp)并选取最优tp点，在USMV
i逃逸局部最优的过程中，仍然实时参与BS判定，继续评估独立覆盖与协同分区的优先级。
在一些可选的实施方案中，步骤(4)包括：
根据
所有子区域P
i的USMV
i均传回FN
i时，则判定整个任务区域P覆盖任务结束，通过探测的全部环境信息，复查遗漏区域，生成覆盖率信息。
按照本发明的另一方面，提供了一种计算机可读存储介质，其上存储有计算机程序，所述计算机程序被处理器执行时实现上述任一项所述方法的步骤。
总体而言，通过本发明所构思的以上技术方案与现有技术相比，能够取得下列有益效果：
本发明借鉴传统覆盖路径规划方法，深入开展多无人测量船艇协同覆盖路径规划研究，设计了多艘无人测量船艇覆盖路径规划方法(Cooperative Coverage IBA*，CCIBA*)，为无人测量船艇规划出高效率、高质量的扫测路径。仿真试验结果显示，CCIBA*在路径长度、转向次数、单元数及覆 盖率等方面性能相比现有方法均有显著提升。
图1是本发明实施例提供的一种多艘无人测量船艇覆盖路径规划方法的流程示意图；
图2是本发明实施例提供的另一种多艘无人测量船艇覆盖路径规划方法的流程示意图；
图3是本发明实施例提供的一种典型行为策略示意图；
图4是本发明实施例提供的一种USMV
i任务分解流程图。
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。此外，下面所描述的本发明各个实施方式中所涉及到的技术特征只要彼此之间未构成冲突就可以相互组合。
本发明的目的是提供一种多艘无人测量船艇覆盖路径规划方法CCIBA*，CCIBA*算法是在IBA*(Improved BA*)的基础上的拓展，CCIBA*和IBA*都是在传统的BA*算法上的改进，提升无人测量船艇复杂作业环境下覆盖率和覆盖效果，提高无人测量船艇的作业效率。为使本发明的上述目的、特征和优点能够更加明显易懂，下面结合附图和具体实施方式对本发明作进一步详细的说明。
如图1所示为本发明实施例提供的一种面向多艘无人测量船艇覆盖路径规划方法CCIBA*的流程示意图，该方法包括：O阶段、
级地图阶段、
级地图阶段及E阶段。
根据上述4个阶段将CCIBA*分为2个过程：离线规划和在线规划。
根据离线规划过程，基于任务性能划分子区域，并建立区域分割、回 溯转移、区域交换和障碍物联合识别等4种典型的协同行为策略。
在线规划具体包括：扫测场景任务分解及扫测场景地图更新。
具体地，如图2所示为本发明实施例提供的另一种面向多艘无人测量船艇覆盖路径规划方法CCIBA*的流程示意图，具体包括以下步骤：
S101：O阶段：在初始化阶段导入静态地图，根据静态地图初始化栅格状态，同步建立子地图与总地图，并基于任务性能分别对子地图和总地图进行区域划分；
其中，静态地图用于反映环境信息，也就是无人测量艇航行地图(海图或者江图)。子地图和总地图都是反映了测量艇的航行环境信息，子地图表示栅格化的静态地图使用CCIBA*算法进行区域划分后形成的区域地图，总地图表示子地图的整合与迭代。
在本发明实施例中，基于任务性能分别对子地图和总地图进行区域划分，包括：
(1)多无人船艇：建立多USMV集合，U＝{USMV
i|1≤i≤I}，I表示USMV数量，协同覆盖的核心目标是使i艘USMV在充分发挥效率的前提下实现对整体任务区域P全部遍历；
(2)任务性能：根据USMV
i个体的性能或执行覆盖任务的能力，提出任务性能指数H
i,i＝1,...I，其大小取决于USMV携带的传感器性能、任务职能及能耗限制等，且
(3)区域划分：根据USMV数目将整体任务区域P划分为I个部分，其中，每个部分对应一个USMV所处区域，各部分以其所占面积百分比表示，其中，各部分表示为：P
i,i＝1,...I，0＜P
i＜1且
(4)栅格限制：规定整体任务区域P的自由空间P
F中的每个栅格α， 至少被任一USMV
i执行过扫描任务：
其中，由0＜P
i＜1且
确定自由空间，Y(α,i)表示栅格限制，
表示BL级地图中t时刻下的栅格α赋值。
例如，
obs表示障碍物；
fz表示禁区；
exp表示已完成测深任务的自由空间；
ue表示未完成测深任务的自由空间。
(5)规划目标：对于多无人船艇协同覆盖，主要考虑以下因素：整体覆盖路径、整体覆盖时间、单体覆盖性能及整体覆盖率：
其中，
表示多艇覆盖总体代价模型，k
1表示覆盖路径代价系数，k
2表 示覆盖时间代价系数，P
i(d
cost)表示P
i区域预估覆盖路径，P
i(t
cost)表示P
i区域预估覆盖时间。
首先根据USMV
i的性能指数H
i估算初始任务区域的d
cost和t
cost，其中，d
cost表示覆盖路径，t
cost表示覆盖时间，d
cost将根据障碍物的分布情况进行进一步修正，t
cost则在考虑USMV携带装备的情况下调整，最终输出重新分配后的子区域。
S102：
级地图阶段：根据子地图
与总地图
中各个子区域P
i的USMV
i输出自身位置信息ω及障碍物信息η，传递给
并更新
然后进行路径规划，寻找目标点tp；
其中，BL
0,…BL
L代表各个动态地图层级BaseLayer，L为最高层级，总地图为
和子地图为
S103：
级地图阶段：陷入局部最优时，则向上逐层更新地图层级，并在对应层级中寻找目标点tp，进行BS判定，并向子区域P
i的USMV
i发送tr指令，其中，BS判定表示协同行为策略判定，tp表示USMV下一目标点所处位置的栅格索引值，tr指令表示USMV处于Travel状态，达到局部最优后的非正常任务状态；
在本发明实施例中，定义行为策略列表：BS∈{ex
1,ex
2,ex
3,ex
4}，ex
1,ex
2,ex
3,ex
4分别对应协同行为策略中区域分割、回溯转移、区域交换和障碍物联合识别4种情形。路径规划优先判定BS，若符合任一情形则输出te或th状态，涉及跨域则基于
规划输出tp
m；若不符合BS任一情形则独立执行路径规划，输出tn或tc状态，其中，tn表示指导USMV处在Normal状态，使其在子区域内执行正常覆盖任务，tc表示指导USMV开始测深任务。
在一些可选的实施方案中，典型的协同行为策略具体包括：
如图3所示，其中虚线代表区域划分边界，不规则图形代表障碍物，点划线表示协同行为策略涉及到的区域交换或重分配。
如图3中(a)所示，区域分割场景中涉及小区域临时分配及子地图更新。对于P
2区域而言，USMV进入由障碍物及区域边界形成的小型Area区域，会面临两方面的潜在损失：其一，根据IBA*算法的障碍物处理策略，进入该区域时受到狭长形地形影响，绕障的成本增加；其二，在不干涉的情况下，进入该区域可能陷入局部最优。在P
1区域中障碍物边缘初步识别的情况下，该策略将P
2中的小型Area区域纳入P
1区域，使USMV在保证连续覆盖动作的情况下，“顺势”执行Area区域覆盖任务。由于该区域面积较小，对两者的任务分配量影响不大，在完成时间方面基本不变。
图3中(b)所示，回溯转移场景中涉及路径方向趋势变化导致的回溯区域。在多USMV协同规划中，受制于子区域各自独立的覆盖更新过程，IBA*算法会产生潜在的回溯区域。在该场景中，P
1区域中的USMV
1依据IBA*算法，从起始位置开始后不久开始绕障动作，从此时直到该USMV
1在左下角区域出界，Area区域仍处于未探索覆盖的状态。所以该策略将Area区域划入P
2区域中，使该区域中的USMV
2继续进入Area区域执行额外的覆盖动作，减少了USMV
1的回溯成本。
如图3中(c)所示，区域交换场景涉及较大区域的交换分配。由于障碍物和边界影响，有较大区域被割裂于P
2区域，继续执行A
rea_2区域任务会导致P
2区域中USMV
2的路径成本和计算成本都增加，而此时A
rea_2区域恰好位于P
1区域的主要覆盖路径方向，A
rea_1区域位于P
2区域的主要覆盖路径方向。因此，该策略将P
1、P
2区域中的A
rea_1和A
rea_2做了交换。此种情况下，覆盖时间及任务量基本不变，基于大致相同的绕障成本，对路径长度的影响也较小。
如图3中(d)所示，障碍物联合识别场景主要针对障碍物的处理。由于独立的子区域地图更新，单独的S
P_1及S
P_1段的绕障路径对于各USMV来 说均不完整，判定障碍物则可能出现遗漏，进而影响总区域地图的更新，所以在覆盖任务执行的同时，额外加入障碍物联合判别的过程。
在一些可选的实施方案中，扫测场景任务分解包括：
首先对栅格任务分解做出定义：
其中，G
m表示总地图栅格列表，
表示总地图栅格个体空间，N表示栅格最大个数，
表示基于总体栅格列表G
m的总体任务，R
i表示编号为i的分任务，I表示P
i任务数上界，与参与任务的USMV数目一致，上标m没有具体的物理含义。
如图4所示，具体内容如下：
(1)状态定义：状态为多艇覆盖路径规划基本状态，反映任务总体流程及内部调整：
S
m＝{O,Q
ini,Q
re,E,COM}
其中，S
m表示总体状态列表，O表示状态开始，Q
ini表示初始任务分配，Q
re表示协调任务分配，E表示结束状态，COM表示计算状态。
(2)回溯列表：
ξ＝{ξ
i:i＝1,2...I}
其中，ξ表示回溯列表，ξ
i表示各子区域回溯列表。
(3)子区域信息：
其中，
表示USMV
i在所处的当前子区域中的区域测深任务状态，其中，FN代表Finished，即已完成，UFN则代表Unfinished，即未完成。
(4)USMV控制指令：
tp
m∈{1,...N
m}
OC
m∈{tn,te,th}
其中，tp
m表示USMV下一目标点所处位置在总地图中的栅格索引值，N
m表示自然数集，OC
m表示总地图中的USMV任务指令，相比子区域权限和优先级更高；tn表示指导USMV处在正常状态，使其在子区域内执行正常覆盖任务；te表示指导USMV开始切换区域，协调区域间的覆盖任务；th表示指导USMV在新的区域继续覆盖任务；
在开始阶段，初始化系统状态列表S。O状态开启后，首先是Q
ini状态开始，将任务区域初始化，根据任务性能评估，大致划分各USMV
i的任务区域。此时输出tn指令给各个USMV
i，根据IBA*算法在其内部完成子区域覆盖任务，记为COM状态。USMV
i不断记录及反馈ω和η，同时实时生成障碍物信息。根据协同行为匹配，若此时满足重分配条件，则将系统切换至Q
re状态，开始对子区域重新分配，受影响的USMV
i则调整为te状态，由覆盖路径规划算法生成tp
m，暂时跳出原区域，到达指定起始点后，指导开启th状态。USMV
i则在每一区域行动中，记录所经历栅格的状态值CS及P
i区域的状态值
在一些可选的实施方案中，扫测场景地图更新包括总地图更新和各子区域地图更新两部分组成，其中总地图拥有更高的优先级及权限，可在必要流程时进行干涉。
子区域地图更新流程均为独立运行状态，各个USMV
i在行动中同时更新总地图
和子地图
经过P
i和R
i分配区域和任务，各个
独立更新完成多USMV覆盖任务，
主要作用于区域间USMV
i间的协同行为，使USMV
i在子区间通过升级地图层级寻找目标点时，有更合理的选择，从 而节省总体的覆盖时间，降低tr状态和te状态对路径长度的消极影响。
具体内容如下：
(1)初始化建模
参考IBA*算法中的地图层级BaseLayer建立方式，仍在全局地图中首先建立精细度最高的栅格地图层级
随后，在
基础上继续建立各子区间的地图层级
其具体包含领域则由总体区域P的初始化划分决定。在
和
层级建立的基础上，继续执行升级指令。
其中，
表示包含所有层级的多艇覆盖总地图栅格列表，
表示
中的栅格个体空间，N
ml表示
栅格最大个数，ml表示地图层级，mL表示最高层级。
(2)
级地图建模与赋值
初始化
级地图。在对
级地图初始化赋值后，将继续开展各个
层级地图的赋值，其势能分配将从各个P
i区间独立开启，因此各个栅格
将拥有2个势能值。但此过程并不会明显增加计算量，一方面两者有着直接且简单的换算关系，另一方面
不会像各个P
i区间的0级地图一样在绝大部分时间处于激活状态，而仅出现于USMV
i区域协调转移的过程。
对于未知障碍物，由于单USMV
i在独立的P
i区间更新GT_list＝{obs,exp,fz,ue}，若其处于子区域边界，则会出现识别不完整的现象。此时首先使用Bresenham算法将已识别障碍物部分轮廓的边线光栅化为帧缓存中像素，再引入Flood Fill算法对其识别结果进行处理。完成
的 障碍物更新后，信息将传递给各个
层级地图。
S104：E阶段：若最高层级仍未找到目标点，检查各个
判定结束。
在一些可选的实施方案中，步骤S101中的O阶段包括：
起始时各艘无人测量船艇均处于默认起始位置，状态为O，建立静态地图的坐标转换栅格索引，分别在各子地图开展栅格状态更新，并依次更新全部地图的0～L级的赋值，USMV
i输出tn指令，与此同时，USMV
i记录及传递自身位置ω及障碍物信息η，各个USMV
i开始独立更新各自的栅格状态列表GT_list，开始协同覆盖任务。
在一些可选的实施方案中，步骤S102中的
级地图阶段具体包括：
在
级地图阶段对各个子地图
逐行赋予势能优先级，保证各子地图中USMV
i的完整覆盖路径；
若BV
ω＞0且
则与单USMV的IBA*算法行动一致，通过潜在代价值J(tp)计算选择相对最优路径，同样的，若ω
N及ω
S中的一侧临近障碍物，则优先选取临近障碍物的ω
N或ω
S方位，通过潜在代价值J(tp)计算选择相对最优路径完成各个区间P
i的绕障路径，同时开启ex
4过程，ω表示USMV当前所处位置的栅格序列数，BV
ω是指BL最高层地图中栅格序列数ω的赋值；
其中，将USMV在栅格地图中的探测领域记为D
0(ω)，ω∈D
0(ω)，D
0(ω)中包含了USMV当前位置能感知到的所有栅格信息。对于D
0(ω)中的任一栅格α
0，若与ω的连线不经过fz或obs状态栅格，且自身势能值为正值，则将其集合定义为优先领域
定义D
0(ω)中位于北、南两个方向的栅格为ω
N及ω
S。
若BV
ω＞0，ω
N及ω
S中有且只有一侧为ue状态，另一侧为禁区，则开启tc指令，以指导USMV
i开始测深任务，同时更新
和
若BV
ω＝0,
则USMV
i开始转向下一阶段的遍历，将F
0中
值最大的α
0作为tp点，α
0表示栅格索引；
若以上情形均判定不符，则认定USMV
i此时处于局部最优的状态，在升级地图层级前，进行BS判定，若符合协同策略，则开始运行预设动作，输出te指令并更新子地图，重新分配子区域P
i；若不符合BS中的任意一种情形，则开启高BL级地图阶段开始寻径，输出tr指令。
在一些可选的实施方案中，步骤S103中的
级地图阶段具体包括：
在
级地图阶段，逐级提高地图等级，在高级地图中继续寻找势能值最大的地图栅格，同时计算其潜在代价值J(tp)并选取最优tp点，在USMV
i逃逸局部最优的过程中，仍然实时参与BS判定，继续评估独立覆盖与协同分区的优先级。
在一些可选的实施方案中，步骤S104中的E阶段具体包括：
E阶段即结束阶段，根据
所有子区域P
i的USMV
i均传回FN
i时，则判定整个任务区域P覆盖任务结束，通过探测的全部环境信息，复查遗漏区域，生成覆盖率信息。
本发明的CCIBA*方法在路径长度、转向次数以及覆盖率等方面的性能，依次与传统的Boustrophedon算法、BA*算法相比，在转向次数方面分别减少了约16.5％、5.1％；单元个数分别减少了58.3％、44.4％；覆盖率分别提升了约2.1％、7.6％。在保证完整覆盖的前提下，路径长度与BA*算法相比未显著增加，比达成完整覆盖的Boustrophedon算法减少了约10.76％。
本申请还提供一种计算机可读存储介质，如闪存、硬盘、多媒体卡、卡型存储器(例如，SD或DX存储器等)、随机访问存储器(RAM)、静 态随机访问存储器(SRAM)、只读存储器(ROM)、电可擦除可编程只读存储器(EEPROM)、可编程只读存储器(PROM)、磁性存储器、磁盘、光盘、服务器、App应用商城等等，其上存储有计算机程序，程序被处理器执行时实现方法实施例中的多艘无人测量船艇覆盖路径规划方法。
需要指出，根据实施的需要，可将本申请中描述的各个步骤/部件拆分为更多步骤/部件，也可将两个或多个步骤/部件或者步骤/部件的部分操作组合成新的步骤/部件，以实现本发明的目的。
本领域的技术人员容易理解，以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。
Claims (9)
- 一种多艘无人测量船艇覆盖路径规划方法，其特征在于，包括：(1)在初始化阶段导入静态地图，根据静态地图初始化栅格状态，同步建立子地图与总地图，并基于任务性能分别对子地图和总地图进行区域划分，其中，静态地图用于反映环境信息，子地图表示栅格化的静态地图进行区域划分后形成的区域地图，总地图表示子地图的整合与迭代；(2)根据子地图与总地图
中各个子区域P i的USMV i输出自身位置信息ω及障碍物信息η，传递给
并更新
然后进行路径规划，寻找目标点tp；
(3)陷入局部最优时，则向上逐层更新地图层级，并在对应层级中寻找目标点tp，进行BS判定，并向子区域P i的USMV i发送tr指令，其中，BS判定表示协同行为策略判定，tp表示USMV下一目标点所处位置的栅格索引值，tr指令表示USMV处于Travel状态，达到局部最优后的非正常任务状态；(4)若最高层级仍未找到目标点，检查各个判定结束，其中，
表示USMV i在所处的当前子区域P i中的区域测深任务状态，其中，FN i代表已完成，UFN i代表未完成。
- 根据权利要求1所述的方法，其特征在于，步骤(1)包括：起始时各艘无人测量船艇均处于默认起始位置，状态为O，建立静态地图的坐标转换栅格索引，分别在各子地图开展栅格状态更新，并依次更新全部地图的0～L级的赋值，USMV i输出tn指令，与此同时，USMV i记录及传递自身位置ω及障碍物信息η，各个USMV i开始独立更新各自的栅格状态列表GT_list，开始协同覆盖任务，其中，tn表示指导USMV处在正常状态，使其在子区域内执行正常覆盖任务。
- 根据权利要求1所述的方法，其特征在于，定义行为策略列表：BS∈{ex 1,ex 2,ex 3,ex 4}，ex 1,ex 2,ex 3,ex 4分别对应协同行为策略中区域分割、回溯转移、区域交换和障碍物联合识别4种情形。
- 根据权利要求3所述的方法，其特征在于，路径规划优先判定BS，若符合任一情形则输出te或th状态，涉及跨域则基于规划输出tp m，若不符合BS任一情形则独立执行路径规划，输出tn或tc状态，其中，tp m表示USMV下一目标点所处位置在总地图中的栅格索引值，te表示指导USMV开始切换区域，协调区域间的覆盖任务，th表示指导USMV在新的区域继续覆盖任务。
- 根据权利要求1所述的方法，其特征在于，基于任务性能分别对子地图和总地图进行区域划分，包括：建立多USMV集合，U＝{USMV i|1≤i≤I}，I表示USMV数量，协同覆盖的核心目标是使i艘USMV在充分发挥效率的前提下实现对整体任务区域P全部遍历；根据USMV i个体的性能或执行覆盖任务的能力，提出任务性能指数H i,i＝1,...I，其大小取决于USMV携带的传感器性能、任务职能及能耗限制等，且
根据USMV数目将整体任务区域P划分为I个部分，其中，每个部分对应一个USMV所处区域，各部分以其所占面积百分比表示，其中，各部分表示为：P i,i＝1,...I，0＜P i＜1且
规定整体任务区域P的自由空间P F中的每个栅格α，至少被任一USMV i执行过扫描任务：
其中，由0＜P i＜1且确定自由空间，Y(α,i)表示栅格限制，
表示BL级地图中t时刻下的栅格α赋值；
对于多无人船艇协同覆盖，主要考虑整体覆盖路径、整体覆盖时间、单体覆盖性能及整体覆盖率，首先根据USMV i的性能指数H i估算初始任务区域的d cost和t cost，其中，d cost表示覆盖路径，t cost表示覆盖时间，d cost将根据障碍物的分布情况进行进一步修正，t cost则在考虑USMV携带装备的情况下调整，最终输出重新分配后的子区域，其中，表示多艇覆盖总体代价模型，k 1表示覆盖路径代价系数，k 2表示覆盖时间代价系数，P i(d cost)表示P i区域预估覆盖路径，P i(t cost)表示P i区域预估覆盖时间。
- 根据权利要求1至5任意一项所述的方法，其特征在于，步骤(2)包括：在级地图阶段对各个子地图
逐行赋予势能优先级，保证各子地图中USMV i的完整覆盖路径；
若BV ω＞0且则通过潜在代价值J(tp)计算选择相对最优路径，同样的，若ω N及ω S中的一侧临近障碍物，则优先选取临近障碍物的ω N或ω S方位，通过潜在代价值J(tp)计算选择相对最优路径完成各个 区间P i的绕障路径，同时开启ex 4过程，ω表示USMV当前所处位置的栅格序列数，BV ω是指BL最高层地图中栅格序列数ω的赋值；将USMV在栅格地图中的探测领域记为D 0(ω)，ω∈D 0(ω)，D 0(ω)中包含了USMV当前位置能感知到的所有栅格信息，对于D 0(ω)中的任一栅格α 0，若与ω的连线不经过fz或obs状态栅格，且自身势能值为正值，则将其集合定义为优先领域
定义D 0(ω)中位于北、南两个方向的栅格为ω N及ω S；
若BVω＞0，ω N及ω S中有且只有一侧为ue状态，另一侧为禁区，则开启tc指令，以指导USMV i开始测深任务，同时更新和
若则USMV i开始转向下一阶段的遍历，将F 0中
值最大的α 0作为tp点，α 0表示栅格索引；
若以上情形均判定不符，则认定USMV i此时处于局部最优的状态，在升级地图层级前，进行BS判定，若符合协同策略，则开始运行预设动作，输出te指令并更新子地图，重新分配子区域P i；若不符合BS中的任意一种情形，则开启高BL级地图阶段开始寻径，输出tr指令。 - 根据权利要求6所述的方法，其特征在于，步骤(3)包括：在级地图阶段，逐级提高地图等级，在高级地图中继续寻找势能值最大的地图栅格，同时计算其潜在代价值J(tp)并选取最优tp点，在USMV i逃逸局部最优的过程中，仍然实时参与BS判定，继续评估独立覆盖与协同分区的优先级。
- 根据权利要求7所述的方法，其特征在于，步骤(4)包括：根据所有子区域P i的USMV i均传回FN i时，则判定整个任务区域P覆盖任务结束，通过探测的全部环境信息，复查遗漏区域，生成覆盖率信息。
- 一种计算机可读存储介质，其上存储有计算机程序，其特征在于， 所述计算机程序被处理器执行时实现权利要求1至8任一项所述方法的步骤。
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| CN112113571B (zh) | 2021-08-17 |
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